ICME 12, TSG 37Theoretical issues in mathematics educationTheoretical issues are of major importance for the field of mathematics education as for any scientific field. This is especially important because compared to other fields mathematics education is rather a young research area that often builds on scientific knowledge of neighboring fields. Therefore it is important to develop theories specifically meeting the needs of mathematics education. Continuing the work carried out in previous ICMEs, this TSG is expected to provide the participants with an up-to-date vision of the state of the reflection regarding the theoretical questions and underpinnings of the field, and at the same time stimulate insightful exchanges and discussions. It is expected to pay specific attention to the diversity of theoretical approaches existing in the field and to the efforts undertaken to address this diversity, to the theoretical advances and debates resulting from the efforts made for improving the relationships between research and practice, and to the influence of contexts and cultures on the ways in which theories are developed and used.

Topic: (a) Theories from outside mathematics educationo Identifying theories particularly suitable for use in mathematics education (and those that are not);o Contrasting the treatment of particular constructs relevant to mathematics education (e.g. "mathematical objects") within two or more theories;o Suggesting inadequacies in the capacity of currently available theories to meet the needs of mathematics education and recommending what developments are required.

Central question: What theories do we need for mathematics education?Presentation One (20 min)Articulating philosophical theories to analyze the field of EthnomathematicsGelsa Knijnik,(Unisinos, Brazil, gelsak@unisinos.br)Presentation Two (20 min)From knowledge to value: Towards an economic theorizationAlexandre Pais,(Department of Learning and Philosophy, Denmark, xande@learning.aau.dk)Paola Valero,

(Aalborg University, Denmark, paola@learning.aau.dk)

Discussion (20 min)

What kind of theories do we need in mathematics education? What do they have to cover?Session 2 Wednesday, July 1110:00-11:30Chaired by David Clarke and Minoru OhtaniTopic: (b) Conditions for theory use and developmento Interrogating the role and function of theories in mathematics education (and mathematics education research) with specific examples;o Exploring the adequacy of a particular theory to provide insight into two or more different contexts or issues in mathematics education;o Discussing the methodological entailments of the selection of particular theories in the process of research design.

Central question: What are the roles and functions for the use of theories?Presentation One (20 min)Vygotskian theory and Mathematical LearningAlbert Lillie,(Boston College, United States, albertli@bc.edu)Presentation Two (20 min)Toward building a theory of "Lived and living mathematical experiences"Larry Hatfield,(University of Wyoming, United States, lhatfiel@uwyo.edu)Presentation Three (20 min)Abstract, Concrete, and Embodied: An Embodied Cognition Perspective of Mathematics EducationDragan Trninic,(University of California, United States, trninic@berkeley.edu)Hee-Jeong Kim,(Berkeley, United States, hj_kim@berkeley.edu)

Discussion (30 min)

What are roles and functions for the use of theories? What do theories for Mathematics Education have to cover?

Session 3 Friday, July 1310:30-12:00Chaired by Angelika Bikner-Ahsbahs and Gelsa Knijnik)Topic: (c) Diversity of theories within mathematics educationo Addressing the challenge of utilising the results of research studies in mathematics education undertaken using different theories;o Networking strategies (such as comparing, contrasting combining, coordinating, integrating, synthesising) designed to provide heightened insight into a complex setting;o Reporting or exploiting examples of the networking of theories concerning their limits and potential for advancing the field of mathematics education.

Central question: How can we deal with different theories in a scientific way?Presentation One (20 min)Alternative theoretical perspectives in and for mathematics educationRuhama Even,(Weizmann Institute of Science, Israel, ruhama.even@weizmann.ac.il)Presentation Two (20 min)What is a mathematical object? Looking at objects from two theoretical perspectivesMaria Trigueros,(Instituto Tecnolofico Autonomo de Mexico, Mexico, trigue@itam.mx)Vicenc Font,(Universitat de Barcelona, Spain, vicencfont@ono.com)Edelmira Badillo, (Universitat Autonoma de Barcelona, Spain, Edelmira.Badillo@uab.cat)Norma Rubio, (Pontificia Universidad Catolica del Peru, Peru, nrubio@pucp.edu.pe)Presentation Three (20 min)Complexity of Dialogue between theories: Difficulties and benefitsIvy Kidron,(Jerusalem College of Technology, Israel, ivy@jct.ac.il)John Monaghan, (University of Leeds, United Kingdom, J.D.Monaghan@education.leeds.ac.uk)

(Ewha Women's University, Korea, meant530@naver.com)Session 4 Saturday, July 1410:00-11:30Chaired by David Clarke and Angelika Bikner-AhsbahsCentral questions:What kind of theories do we need in mathematics education?What are the affordances they have to fulfill?What are the conditions, the roles and the functions of theory use and development?How do we deal with the diversity of theories in a scientific fruitful way?Short Presentation One (10 min)Philosophical aspects present in questions regarding mathematics technology and educationMaurício Rosa,(Lutheran University of Brazil, Brazil, mauriciomatematica@gmail.com)Short Presentation Two (10 min)Visuality and mathematical visualization: seeking new frontiersClaudia Flores,(Federal University of Santa Catarina, Brazil, crf@mbox1.ufsc.br)Short Presentation Three (10 min)Mathematical imagination and its significance for Mathematics Education